Question

geometry 452 cw/hwsimilarity theorems 2-11-26name1) draw two triangles that are similar by the sss similarity theorem but not congruent. do not include any angles. you must give information about all sides.2) draw two triangles the are not similar by the sss similarity theorem. do not include any angles. you must give information about all sides3) draw two triangles that are similar by the sas similarity theorem but not congruent. each triangle must have only 1 angle and only two sides marked.) draw two triangles that are not similar by the sas similarity theorem but not congruent. each triangle must have only 1 angle and only two sides marked.

Explanation:

1. For SSS similar (non-congruent): Use triangles with side lengths in a consistent non-1 scale factor, no angles marked.
2. For non-SSS similar: Use triangles with side length ratios that are not equal across all pairs, no angles marked.
3. For SAS similar (non-congruent): Use triangles with one equal included angle, and the two surrounding sides in a consistent non-1 scale factor.
4. For non-SAS similar: Use triangles with either non-equal included angles, or equal angles but side ratios that do not match.

Answer:

1. Triangle 1: Sides marked 2, 3, 4

Triangle 2: Sides marked 4, 6, 8
(Ratio of sides: $\frac{4}{2}=\frac{6}{3}=\frac{8}{4}=2$, so SSS similar, not congruent)

1. Triangle 1: Sides marked 2, 3, 4

Triangle 2: Sides marked 2, 3, 5
(Ratios: $\frac{2}{2}=1$, $\frac{3}{3}=1$, $\frac{5}{4}=1.25$; ratios are not equal, so not SSS similar)

1. Triangle 1: Included angle $50^\circ$ between sides 2 and 3

Triangle 2: Included angle $50^\circ$ between sides 4 and 6
(Ratio of sides: $\frac{4}{2}=\frac{6}{3}=2$, included angle equal, so SAS similar, not congruent)

1. Triangle 1: Included angle $50^\circ$ between sides 2 and 3

Triangle 2: Included angle $60^\circ$ between sides 4 and 6
(Included angles are not equal, so not SAS similar; triangles are not congruent)